Two vectors overrightarrow{ A } and overrightarrow{ B } have equal magnitudes. If magnitude of overr

English

Gujarati

Hindi

3-1.Vectors

medium

Two vectors $\overrightarrow{ A }$ and $\overrightarrow{ B }$ have equal magnitudes. If magnitude of $\overrightarrow{ A }+\overrightarrow{ B }$ is equal to two times the magnitude of $\overrightarrow{ A }-\overrightarrow{ B }$, then the angle between $\overrightarrow{ A }$ and $\overrightarrow{ B }$ will be .......................

A

$\sin ^{-1}\left(\frac{3}{5}\right)$

B

$\sin ^{-1}\left(\frac{1}{3}\right)$

C

$\cos ^{-1}\left(\frac{3}{5}\right)$

D

$\cos ^{-1}\left(\frac{1}{3}\right)$

(JEE MAIN-2022)

Solution

$\left(a^{2}+b^{2}+2 a b \cos \theta\right)=4\left(a^{2}+b^{2}-2 a b \cos \theta\right)$

put $a$ = $b$ we get

$2 a^{2}+2 a^{2} \cos \theta=8 a^{2}-8 a^{2} \cos \theta$

$\cos \theta=\frac{3}{5}$

Standard 11

Physics

Share

Similar Questions

The three vectors $\overrightarrow A = 3\hat i – 2\hat j + \hat k,\,\,\overrightarrow B = \hat i – 3\hat j + 5\hat k$ and $\overrightarrow C = 2\hat i + \hat j – 4\hat k$ form

medium

If $a$ and $b$ are two units vectors inclined at an angle of $60^{\circ}$ to each other, then

medium

The vectors $\vec{A}$ and $\vec{B}$ are such that

$|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$

The angle between the two vectors is

hard

(AIPMT-2006)

How many minimum number of coplanar vectors having different magnitudes can be added to give zero resultant

easy

Given below in Column $-I$ are the relations between vectors $\vec a \,$ $\vec b \,$ and $\vec c \,$ and in Column $-II$ are the orientations of $\vec a$, $\vec b$ and $\vec c$ in the $XY-$ plane. Match the relation in Column $-I$ to correct orientations in Column $-II$.

Column $-I$ Column $-II$

$(a)$ $\vec a \, + \,\,\vec b \, = \,\,\vec c $ $(i)$ Image

$(b)$ $\vec a \, – \,\,\vec c \, = \,\,\vec b$ $(ii)$ Image

$(c)$ $\vec b \, – \,\,\vec a \, = \,\,\vec c $ $(iii)$ Image

$(d)$ $\vec a \, + \,\,\vec b \, + \,\,\vec c =0$ $(iv)$ Image

medium